Voluntariness and the Coase Theorem

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Voluntariness and the Coase Theorem
Tore Ellingseny
and Elena Paltsevaz
16 February 2011
Abstract
The paper investigates t...

1 Introduction
A modern statement of the Coase Theorem is that voluntary bargaining su ces to
attain e cient outcomes if (...

electricity.3
Both households would like to have an electricity cable to the island.
Suppose cables come in one size but i...

P N
P 8; 8 5; 10
N 10; 5 0; 0
Figure 1: The participation decision
The game has two pure strategy equilibria, (P,N) and (N...

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(1973). A typical illustration was the relationship between a bee keeper and the owner
of an apple orchard. The presence o...

coalitions. A crucial di erence is that Bloch and Gomes, like other work in this vein,
assume that there is always at leas...

2 The simultaneous membership model
A group of identical players are to decide on production of and access to a club good....

The quality of the club good is assumed to be xed after stage 2. Thus, it depends
only on total stage 2 contributions. Sin...

of member i must thus solve the problem
max
ej
2m
X
ei
i2M
"
!1=2
ej;
which implies that
X
ei = m2
+ ":
Incentives to ente...

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Proof. First, derive the quality of club good produced at date 1, conditional on m
players having decided to join the club...

(see Appendix 1 for details). The quality of the club good produced in equilibrium q
is given by formula (3) for m = m :
W...

Proof. Suppose that at date 0 player n expects all other n 1 players to join the club.
From formula (2) it follows that a ...

While the results were derived under the assumption that club members divide
utility equally, ine ciency can only get wors...

Although the analysis becomes somewhat technical, the ine cient outcome rests on
two elementary arguments. First, early mo...

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Note that the payments to the club members i 2 M ( n 1) are already set when
the game reaches node X and do not depend on ...

join if o ered the utility emanating from staying outside, and since both parties can
gain from a higher quality level tha...

Compare the payo of player 1 along In
n 1 and Out
n 1 respectively:
P(1j In
n 1) P(1j Out
n 1) =
0
@V (m0
+ 2)
X
i2M0( n 2...

Lemma 3 If player 1 organizes the club, she does not sign up player i = 2; :::; n 2
in any subgame-perfect equilibrium.
Pr...

Lemma 4 If players i = 1; :::; k 1 choose not to participate in the production of the
public good, and player k < n organi...

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the same result holds for players n 3; :::; 1. So for these parameter values the SPNE
of the game is highly ine cient; the...

this case the club consists of two members, 1 and n; and again produces the quality q:
This completes our characterization...

outsiders' surplus. We think that this objection is intriguing, but does not necessar-
ily resolve the problem. If the clu...

On the other hand, Ellingsen and Paltseva (2011) argue that optimal outcomes are
attainable in Jackson and Wilkie's settin...

[6] Coase, R.H. (1960): The Problem of Social Cost, Journal of Law and Economics
3, 1-44.
[7] Coase, R.H. (1981): The Coas...

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[17] Mas-Colell, A., Whinston, M.D., and Green, J.R. (1995): Microeconomic Theory,
Oxford: Oxford University Press.
[18] M...

A Appendix 1: Proofs.
A.1 Proof of Proposition 1.
Using (4) and (5) equation (6) takes the form
2 ( m + (1 )n) >
( (m + 1)...

and thus m also (weakly) increases in n, the actual increase occurring when em 2 N.
According to formula (3)
q = 2 ( m + (...

B Appendix 2: Multi-round membership negotia-
tions. [Not for publication?]
An objection to the single-round membership ne...

same time, players cannot be forced to sit at the bargaining table. That is, at her move,
in addition to the options of cr...

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general case. Moreover, the nal outcome in the K = 2 case is identical to the K = 1
case.
Lemma 5 If player 1 chooses to o...

Thus, in this case player 1 does not sign player n in the rst round, and player n
chooses to exit. Player j gets signed in...

Suppose that each player 1; :::; i 1 has chosen to exit too. Then we showed above
that player n joins the club, so that th...

Second, suppose that only one player h 2 f1; :::; n 1g waited. If player n chooses
to organize the club, she signs in play...

organizer of the club of size 2; which is in turn higher than the payo of an outsider of
the club of size 1 :
POut
2 > POr...

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Now consider the options of the player n 1: If everyone exited before, she chooses
to organize the club, as this brings he...

Thus, staying outside without exit entails a loss of the rst mover advantage { if
player h < n has chosen to stay, every p...

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